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Solve each continuous exponential growth problem.

24. A savings account balance is compounded continuously. If the interest rate is 3% per year and the current balance is $1727.00, what will the balance be 6 years from now?

Answers

Answer 1

Answer:

$2,067.59

Step-by-step explanation:

To calculate the balance of the savings account, we can use the continuous compounding interest formula:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Interest Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]

Given values:

P = $1,727.00r = 3% = 0.03t = 6 years

Substitute the given values into the formula and solve for A:

[tex]\begin{aligned}A&=1727 \cdot e^{0.03 \cdot 6}\\&=1727 \cdot e^{0.18}\\&=1727 \cdot 1.19721736...\\&=2067.59438...\\&=2067.59\end{aligned}[/tex]

Therefore, the balance of the savings account 6 years from now is $2,067.59.


Related Questions

Each figure below represents a fraction. Which figure is NOT equivalent to the others

Answers

The full question with the answer options is as follows:

Each figure below represents a fraction. Which figure is NOT equivalent to the others?

the answer options are as follows:

a.  [tex]\frac{2}{3}[/tex]

b.  [tex]\frac{4}{6}[/tex]

c.  [tex]\frac{3}{4}[/tex]

d. [tex]\frac{8}{12}[/tex]

Answer:

The correct answer is c:

Step-by-step explanation:

To know when two or more fractions are equivalent, we must multiply the numerator of one fraction by the denominator of the other fraction, the result must be the same value.

[tex]\frac{2}{3} x \frac{4}{6}[/tex] =   (2x6) =12   ;  (3x4)=12

[tex]\frac{2}{3} x \frac{8}{12}[/tex] = (2x12)=24 ;    (3x8) =24

[tex]\frac{4}{6} x \frac{8}{12}[/tex] = (4x12)=48;     (6x8)=48

which sides form a right triangle​

Answers

Answer:

c

Do i get brainliest lol

find the value of x. round to the nearest tenth if needed.

Answers

[tex]6^{2}+8^{2}=x^{2} \\36+64=x^{2} \\100=x^{2} \\x=10[/tex]

PLSSS ANSWER JUST PUT THE NUMBER OF THE QUESTION THEN THE ANSWER PLS HELP ITS OVERDUE AND IM GONNA FAIL 7TH GRADE :(
I WILL GIVE BRAINLIEST EVERYONE KEEPS GIVING ME RANDOM LINKS IM CRYIING :( I WOULD BE SO GRATEFUL IF U HELPED UR A LIFE SAVER

Answers

Answer:

Alright but first

How is this 7th grade stuff?

I thoguh yall were doing algebra. But it kinda looks like it but here’s a brief explanation anyway.

If you dont know a vualure, use other surrounding it to help you sovle this final thingy. Like if its division, multiply. addditon, subtract. multiply, Davison. Just tdo inver properties on both sides and isolate the number that x in it Either be dividing or multiplying. When your left with a final value just solve, whatever thing that lies next to that equal sign is your answer.

2) 6

3) -36

4) 40

5) 9

6) -4

7) 63

8) -48

9) -5

10) -7

The average value of a function f(x, y, z) over a solid region E is defined to be fave = 1 V(E) E f(x, y, z) dV where V(E) is the volume of E. For instance, if ???? is a density function, then ????ave is the average density of E. Find the average value of the function f(x, y, z) = 3x2z + 3y2z over the region enclosed by the paraboloid z = 4 − x2 − y2 and the plane z = 0.

Answers

Answer:

The average function [tex]f_{avg}[/tex] value = 4

Step-by-step explanation:

Given that:

[tex]f(x,y,z) = 3x^2z+3y^2z[/tex]

The enclosed region [tex]z = 4 -x^2 -y^2[/tex] and the plane z = 0.

Over an area E, the average value of a function f(x,y,z) is:

[tex]f_{avg} = \dfrac{1}{V_{E}} \iiint_E f(x,y,z) dV ------ (1)[/tex]

where;

[tex]V_E[/tex] = volume of region E

To find the volume use cylindrical coordinates;

[tex]x=rcos \theta; \ \ \ y = rsin \theta; \ \ \ z = z[/tex]

Then;

E = 0 ≤ r ≤2, 0 ≤ θ ≤ 2π, 0 ≤ z ≤ 4 - r²

[tex]V_E = \int^{2 \pi}_{0} \int^{2}_{0} \int^{4-r^2}_{0} \ rdzdrd \theta[/tex]

[tex]V_E = \int^{2 \pi}_{0} \int^{2}_{0} r(4-r^2) \ drd \theta[/tex]

[tex]V_E = \int^{2 \pi}_{0} \int^{2}_{0} (4r-r^3) \ drd \theta[/tex]

[tex]V_E = \int^{2 \pi}_{0} \Big(2r^2- \dfrac{r^4}{4} \Big)^2_0 \ d \theta[/tex]

[tex]V_E = 4(2 \pi)\\\\ V_E = 8 \pi[/tex]

However, from equation (1):

[tex]f_{avg} = \dfrac{1}{V_E} \iiint_E f(x,y,z) \ dV \\ \\ = \dfrac{1}{8 \pi} \iiint_E (3x^2z + 3y^2 z) dV \\ \\ = \dfrac{1}{8 \pi } \int^{2 \pi}_{0} \int^{2 }_{0} \int^{4 - r^2}_{0} \ \ 3zr^2 \ rdzdrd\theta \\ \\ = \dfrac{3}{8 \pi} \int^{2 \pi}_{0} \int^{2 }_{0} \Big(\dfrac{z^2}{2}\Big)^{4-r^2}_{0} \ r^3 drd\theta \\ \\ = \dfrac{3}{16 \pi} \int^{2 \pi}_{0} \int^{2 }_{0} (4-r^2)^2 \ r^3 \ dr d\theta[/tex]

[tex]= \dfrac{3}{16 \pi} \int^{2 \pi}_{0} \int^{2 }_{0} (16-8r^2 + r^4)r^3 \ dr d\theta \\ \\ = \dfrac{3}{16 \pi} \int^{2 \pi}_{0} \int^{2 }_{0} (16r^3 -8r^5 + r^7) \ dr d \theta \\ \\ = = \dfrac{3}{16 \pi} \int^{2 \pi}_{0} \Big (4r^4 - \dfrac{8}{6}r^6 + \dfrac{r^8}{8} \Big)^2_0 \ d \theta \\ \\ = \dfrac{3}{16 \pi } (2 \pi) \Big (64 - \dfrac{8}{6} \times 64 \times \dfrac{256}{8} \Big) \\ \\ = \dfrac{3}{16 \pi} (2 \pi) (\dfrac{32}{3}) \\ \\ = 4[/tex]

What is the approximate volume of a cylinder with a radius of 7 cam and a height of 4 cm

Answers

Answer:

volume =

[tex] {7}^{2} \times 3.14 \times 2 \times 4[/tex]

Step-by-step explanation:

volume =area of the base circle × height

Identify the 3D shape shown below. Choose 1 answer: A Cone B Cylinder © Sphere​

Answers

Answer:

Cylinder

Step-by-step explanation:

A cone is a 3D triangle with a circular base, and a sphere is a 3D circle

Answer:

CYLIDER

Step-by-step explanation:

ASAP HELPPP NO LINKS! IF THIS IS A FALSE RESPONSE I AM REPORTING

A water cooler in the school office dispenses cone-shaped paper cups. The height of a cup is 5 inches and it has a radius of 2 inches. How many cubic inches of water will it take to fill up the paper cup? Round your answer the nearest hundredth.

Answers

Answer:

37.699 cubic inches of water

Step-by-step explanation:

Volume of a cone is V= 1/3 pi r^2 h

We are given that the height is 5 in and the radius is 2 in.

Plug that into the formula: V= 1/3 pi 2^2 9

1/3 x 4 x 9 = 12

Now we are left with 12 pi.

Use a calculator and multiply 12 by pi to get:

37.699

look at pic 10 pts will mark brainilest hhhionnia

Answers

30 because 18 and the plain goes into 12 which is 30
I think

find the following:1) 30% of 90​

Answers

Answer:

27

Step-by-step explanation:

30/100 ×90 is 27.

it's making me type more but that's the answer :)

Answer:

30%×90

=30/100×90

=27 is the answer of this question

A pelican has a wingspan of 8 wholes 1/5 feet.
An eagle has a wingspan of 6 wholes 2/3 feet.
How much longer is the wingspan
of a pelican?

Answers

Answer:

The wingspan of a pelican is 1 8/15 feet longer than the wingspan of an eagle.

(1 whole 8/15 feet)

Step-by-step explanation:

We'll need to find a common denominator for the fractions. 15 is the lowest number divisible by both 5 and 3, so we'll use 15. For this problem, it's also easier to convert to improper fractions, in my opinion.

Pelican:

8 1/5 = 41/5

41/5 x 3/3 = 123/15

Eagle:

6 2/3 = 20/3

(20/3) x (5/5) = 100/15

Find the difference:

123/15 - 100/15 = 23/15 = 1 8/15

Please let me know if you have questions.

Find the value of x. Round to the nearest degree.

Answers

Its not yet known. We need other numbers and letters!

ANSWER ASAP! NO SCAM LINKS OR REPORTED.

Answers

Answer:

d

Step-by-step explanation:

it would be a parabola not linear

4. What is the measure of each interior angle of
a regular 20-gon?

Answers

Answer:

162

Step-by-step explanation:

please help asap, i will mark as brainliest. please try to find the answer! asap

Answers

1. 14.4 km, 2. 25.2 km, 3. 37.8 km

find the slope of the line that passes through

Answers

Answer:

The answer is in A)

Step-by-step explanation:

Hope it's help you ❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️

13.068 the same as 13.608

Answers

Answer:

No its not

Step-by-step explanation:

13.603 is more then 13.068  

can someone please answer this im so tired man​

Answers

Answer:

3. 7/12

4. 1/3

5.1 1/2

Step-by-step explanation:

Hope this helps and have a great day!!!

Help please!!
Brainliest if right

Answers

Answer:

top and bottom

Step-by-step explanation:

Some help if you can i just need it

Answers

The correct answer is C.

1) Which of the following is a measurement of length? *
O the amount of water in a pool
O the height of a building
how many blocks of concrete cover a sidewalk
O the amount of writing space on a page

Answers

How many blocks of concrete cover the sidewalk

What’s the mean median mode and range of the data set 14,18,12,20

Answers

mean: the average of the values
16

median: the middle when in chronological order
16

range: highest value - lowest value
8

Answer:

....

Step-by-step explanation:

mean: 16

median: 16

there is no mode

range: 8

Put this numbers from least to greatest.

A: 3.2, 0.67, 9, 1.78, 0.651.

please please please please please PLEASE please please please please please please please please please please help me.​

Answers

Answer:

0.651, 0.67, 1.79, 3.2, and 9

Step-by-step explanation:

Answer:

0.651. ,0.67 ,1.78 ,3.2 ,9

Step-by-step explanation:

well if your confused on 0.651 and 0.67 i personally may go for the first two unless if the questions longer

how many different perfect cubes are among the positive actors of 2021^2021

Answers

Answer:

hope this helps :D

Step-by-step explanation:

Perfect cube factors:

If a number is a perfect cube, then the power of the prime factors should be divisible by 3.

Example 1:Find the number of factors of293655118 that are perfect cube?

Solution: If a number is a perfect cube, then the power of the prime factors should be divisible by 3. Hence perfect cube factors must have

2(0 or 3 or 6or 9)—– 4 factors

3(0 or 3 or 6)  —–  3  factors

5(0 or 3)——- 2 factors

11(0 or 3 or 6 )— 3 factors

Hence, the total number of factors which are perfect cube 4x3x2x3=72

Perfect square and perfect cube

If a number is both perfect square and perfect cube then the powers of prime factors must be divisible by 6.

Example 2: How many factors of 293655118 are both perfect square and perfect cube?

Solution: If a number is both perfect square and perfect cube then the powers of prime factors must be divisible by 6.Hence both perfect square and perfect cube must have

2(0 or 6)—– 2 factors

3(0 or 6) —– 2 factors

5(0)——- 1 factor

11(0 or 6)— 2 factors

Hence total number of such factors are 2x2x1x2=8

Example 3: How many factors of293655118are either perfect squares or perfect cubes but not both?

Solution:

Let A denotes set of numbers, which are perfect squares.

If a number is a perfect square, then the power of the prime factors should be divisible by 2. Hence perfect square factors must have

2(0 or 2 or 4 or 6 or 8)—– 5 factors

3(0 or 2 or 4 or 6)  —– 4 factors

5(0 or 2or 4 )——- 3 factors

11(0 or 2or 4 or6 or 8 )— 5 factors

Hence, the total number of factors which are perfect square i.e. n(A)=5x4x3x5=300

Let B denotes set of numbers, which are perfect cubes

If a number is a perfect cube, then the power of the prime factors should be divisible by 3. Hence perfect cube factors must have

2(0 or 3 or 6or 9)—– 4 factors

3(0 or 3 or 6)  —–  3  factors

5(0 or 3)——- 2 factors

11(0 or 3 or 6 )— 3 factors

Hence, the total number of factors which are perfect cube i.e. n(B)=4x3x2x3=72

If a number is both perfect square and perfect cube then the powers of prime factors must be divisible by 6.Hence both perfect square and perfect cube must have

2(0 or 6)—– 2 factors

3(0 or 6) —– 2 factors

5(0)——- 1 factor

11(0 or 6)— 2 factors

Hence total number of such factors are i.e.n(A∩B)=2x2x1x2=8

We are asked to calculate which are either perfect square or perfect cubes i.e.

n(A U B )= n(A) + n(B) – n(A∩B)

=300+72 – 8

=364

Hence required number of factors is 364.

In a walking competition, Marlinda was 15m ahead of Sandra Evliani. Marlinda steps 1m each time Sandra Elviani’s foot steps 0.8m. How many steps does Sandra Elviani have to make to match Marlinda?​

Answers

Answer:

Given that in a walking competition, Marlinda was 15m ahead of Sandra Evliani, and Marlinda steps 1m each time Sandra Elviani's foot steps 0.8m, to determine how many steps does Sandra Elviani have to make to match Marlinda, the following calculation must be performed:

Since Sandra Elviani walks 0.8 meters for every 1 meter that Marlinda walks, and that she has an advantage of 15 meters in the competition, it is impossible that at that rate Sandra can reach her. This is so because for each step of Marlinda, Sandra will be 0.2 meters behind her, increasing the distance (1-0.8).

NO LINKS ONLY ANSWERS (25 POINTS)

Arrange the equations in the correct sequence to rewrite the formula for displacement, d=vt-1/2at^2, to find a. In the formula, d is displacement, v is final velocity, a is acceleration, and t is time.

There is a total of 3 answer slots.

Answers

Answers:

d = v(initial)t + 1/2(at^2)

v(final) = √(v(initial)^2 + 2ad)

a = 2(d-v(initial)t) / t^2

t = -v(initial)±√(v(initial)^2 + 2ad) / a

Answer:

1. vt-d=1/2at^2

2. d-vt=1/2at^2

3. a=2(d-vt)/t^2

Step-by-step explanation:

A dressmaker needs to cut 9-inch pieces of ribbon from rolls of ribbon that are 12 feet in length. How many 9-inch pieces can the dressmaker cut from 5 of these rolls of ribbon?

Answers

Answer:

She can cut 6 nine inch pieces.

Step-by-step explanation:

12x5=60 and 9 goes into 60 6 times which equals 54.

Step-by-step explanation:

i can't help you because that i am no a unit test i am so sorry for not help you

HELP QUICK & NOW PLS
Trapezoid ABCD is inscribed in circle O. Diagonals BD and AC meet at point E and AD is
parallel to BC, as shown.
Select the angles and value that
make a true statement about
trapezoid ABCD.

(fill in equation to the right pls)

Answers

Answer:

I think this would be,

ADE = 180- BCE

I am not sure if this is the right answer, and i am sorry if the answer is wrong, i am just learning about this topic.

Answer:

m<ADC= 180-m<ABC or m<ABC=180-m<ADC

Step-by-step explanation:

Firstly, we need to establish that trapezoid ABCD is an isosceles trapezoid. By doing so, we know that angles opposite one another in an isoseles trapezoid are supplementary. As a result, m<ACD+m<ABC= 180. We can now solve for angle ACD or ABC.

PLEASE ANSWER ASAP! NO SCAM LINKS OR REPORTEd

Answers

Dude I’m getting so many scam links to, it’s so annoying

PLS HELP WILL GIVE BRAINLIEST PLSSSSSSSS
Which point does NOT lie on the graph of the line 6x + 3y = 18?
A. (1, 4)
B. (3, 0)
C. (5, 4)
D. (6, -6)

Answers

Answer:

C

Step-by-step explanation:

6 * 5 = 30

3*4 = 12

30 + 12 = 42

42 does not equal 18

Answer:

The answer is C. (5,4)

Step-by-step explanation:

have a great day.

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